A header is an include file for c and c++ programs (and other program languages too). This type of files have extension .h and are used for some declarations and functions. The kernel headers are the include files for the linux kernel. You will probably need them if you plan to compile programs because many programs use them.
If you are unsure about the need of any package read the .txt file for it if it is official Slackware package. And for the kernel - actually the kernel is what makes from Linux Linux. The common for all of the Linux distributions is that all of them use some version of the linux kernel. If you have the time and the interest you should read additional info about this because it will help you use your linux more efficiently. For example the slackware book is a good place to start for slackers.